The human head is quite heavy. When the body is relaxed in sleep, the weight of the head presses against the pillow with considerable force. If the face is against the pillow when the sleeper turns, the skin of the face is rubbed forcefully across the fabric covering of pillows of the prior art. The continuous trauma of this rubbing over so many hours of sleep in a lifetime is damaging to the skin of some individuals. It is especially injurious to a person after injury or surgery, such as cosmetic surgery. It is preferable to leave injured skin open to the air to promote healing, but bandages may be required to protect the skin from sleeping injury by conventional pillows. The invention reduces trauma to the skin by providing an outer layer of pillow covering that moves freely with the skin by sliding over a slick or slippery under layer that remains unmoving with the pillow itself. U.S. Pat. No. 2,884,652 issued 5/5/59 to Paolicelli and U.S. Pat. No. 2,779,033 issued 1/29/57 to Fountain teach novel pillow coverings that do not address the trauma issue. U.S. Pat. Nos. 4,546,516 and 4,493,866 issued on 10/15/85 and 1/15/85 to Kim teach cosmetic towels with an outer layer that slides on an inner layer for drying without rubbing and U.S. Pat. Nos. 4,615,188 issued 10/7/86 to Hursh and 4,341,096 issued 7/27/82 to Safrit et al. teach socks with a sliding outer surface layer to prevent chafing. However, no prior art addresses the problem of trauma from sleeping on conventional pillows nor the pillows and pillowcases of the instant invention that solve the problem.